The hardest problems in business are the ones that money alone can't solve. A gushing oil leak on the ocean floor is one example. LeBron James is another. When the 25-year-old aspiring "global icon" becomes a free agent on July 1, his price will be fixed. The rules worked out by the National Basketball Assn. owners and players union dictate that as a seven-year veteran, James can receive more than 30 percent of a team's salary cap, which is projected to be $56.1 million next year. The Cleveland Cavaliers, his current employer and hometown team, can offer a six-year contract while the competition can offer only five, but regardless of where he signs, James will have to survive on an average of about $20 million a year.

James is quite a bit more valuable than that. The Cavaliers had the NBA's best regular-reason record this year; should James sign elsewhere, they will immediately sink to the middle of the league pack, if not lower. The psychic blow — to the team, the city, the entire Rust Belt — would be even greater. The pressure to persuade James to stay is enormous. In a press conference the day after the Cavaliers were eliminated from the playoffs, team owner Dan Gilbert, a normally voluble entrepreneur who built the Quicken Loans mortgage empire from the ground up, labored under the load. His voice trailed off at the end of sentences, and he laughed feebly at his own jokes. "We have to ignore the noise," he said flatly. "We are focused on building the best franchise, the best environment, the best place for a long-term situation for LeBron or any free agent that we want to come here."

Gilbert bought the Cavaliers for $375 million in 2005, halfway through James's second year with the team. He has been adamant that he won't beg or grovel for James to stay — and that's a logical negotiating stance. Doing so would acknowledge that the value of his investment rides on the whims of a single employee who is half his age. Guess what? It does anyway. When James joined the team, home attendance at Cavaliers games went up 59 percent. This season, the team sold out all 41 home games for the first time in franchise history, and the Cavaliers were shown on national television as often as the Lakers and Celtics. Gilbert may own the Cavaliers, but James owns Gilbert.

In a 2009 study titled "Should Investors Bet on the Jockey or the Horse?" in The Journal of Finance, Steven Kaplan, an expert on executive compensation at the University of Chicago Booth School of Business, found that the answer, generally, is the horse. "In most businesses, what you find is that the core attribute is not the people, it's the business," he says. "Warren Buffett has a famous saying, which I think is supported by the data: 'When a management with a reputation for brilliance tackles a business with a reputation for bad economics, it is usually the reputation of the business that remains intact.'"

Kaplan's analysis presumes that value is sprinkled somewhat evenly across an organization. LeBron-style problems emerge when one entity is disporportionately responsible for value-creation. Sports franchises are obvious examples, though hardly the only ones.

The economics of the legal profession is also skewed by larger-than-life talent that demands larger-than-life compensation. Twenty years ago, at the law firm Kirkland & Ellis, Fred Bartlit Jr. was LeBron James in pinstripes. Bartlit, now best known for representing George W. Bush in Gore v. Bush in 2000, had distinguished himself as a powerful trial lawyer who attracted big clients. The compensation structure at Kirkland, as at most large firms, however, was based primarily on seniority and hours billed. Frustrated by the difference between his perceived value and his paycheck, Bartlit persuaded Kirkland to adopt a pay-by-results system for him and his group. "I originally thought that the model of getting paid for the value you bring could co-exist within an hourly firm," Bartlit says. But the two systems didn't work together. As a result, Bartlit left Kirkland in 1993 and founded Bartlit Beck Herman Palenchar & Scott.

Bartlit, whose Chicago office uses a two-story basketball court as a conference room, sees the parallels between big-time trial lawyers and big-time basketball players. "I bet there are fewer lawyers who actually try billion-dollar, bet-your-company cases to verdict with consistency than there are big-ticket basketball players," he says. "When we go for interviews on these big cases, we often see the same four or five lawyers. I had one on the West Coast recently, and in the lobby of the hotel as we were getting ready, I saw David Boies (his opponent in Gore v. Bush)."

Boies, adds Bartlit, is another star who could not get what he perceived to be fair value for his services within the culture of an established firm. (Boies famously left Cravath, Swaine & Moore in 1997 to start Boies, Schiller & Flexner.) For Bartlit, this is the natural way of things: Talented lawyers with an appetite for risk eventually feel undervalued enough to strike out on their own.

James doesn't have the option of leaving the Cavaliers for his own firm. While he might one day find himself with the means to buy a team, for now he's restricted to working for the cartel of 30 NBA owners in the much the same way that movie stars are stuck negotiating with the so-called Big Six studios (Warner Bros., Fox, Paramount, Sony, Disney, and NBC Universal). But where NBA owners formally band together under the auspices of a commissioner to protect themselves from the foolish and free-spending among them, studio heads simply keep a common discipline against prodigal spending.

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Still, LeBron problems can emerge when movie stars gain leverage from associations with a hit franchise, as Tobey Maguire did after the original installment of "Spider-Man." After receiving $4 million to star in a movie that grossed $820 million worldwide, Maguire renegotiated his deal to get $17 million for the sequel and $15 million, plus a heavy cut of the gross, for the third. But when the director Sam Raimi balked at a budget for the fourth installment that he considered too low, the studio delayed production and dumped Raimi, Maguire, and his co-star Kirsten Dunst. In an industry where only the most ardent viewers can discern a Ryan Gosling from a Ryan Reynolds, such things are possible, albeit risky. Spider-Man 4 is in limbo, and replacement stars in franchise movies can tank. See "Dumb and Dumberer." Better yet, don't.

If there's a common strategy among successful managers with LeBron problems, it's to stop negotiating and start seducing: What does LeBron James need that money can't buy? "A world-class athlete is fundamentally no different than a world-class scientist," says Michael M. Crow, the president of Arizona State University. "They are interested in finding a way to express everything that they have without limit so that they can gain recognition." President E. Gordon Gee of Ohio State University likens himself to an "institutional psychiatrist," someone who recruits people who would be successful anywhere but require the constant reassurance that their institution believes in them. Reassurance can be time-consuming, and it requires adjustments in organizational culture. On the other hand, it's also free.

Best-selling novelist James Patterson dominates the publishing industry in much the same way James does the NBA. Some titles sell better than his, but no author can compete on volume. Last year Patterson sold 14 million copies while publishing nine new books. He holds the all-time record with more than 50 New York Times best sellers to his name. Patterson is well compensated — Forbes valued his current 17-book deal at $150 million — and money is not terribly important to him. "I'm not particularly interested in squeezing every penny out that I possibly could," he says. Instead, Patterson wants a commitment from his publisher to work hard and make a big deal of everything he does.

Movie studios, naturally, are expert at this kind of pampering. "Tom Cruise has a caterer he's been using since the movie The Firm," says Edward Jay Epstein, author of "The Hollywood Economist" and expert witness in film contract disputes. "If he complains he has a stomachache, you're delaying the movie at a cost of $300,000 a day, so you're not going to screw around with the caterer. Makeup, trainers, security, all that, the star will get." Studios will go so far as to give bit parts to the members of a star's entourage. "The point of these people is to make the star happy and make the movie work, it's not really a negotiation as much as an accommodation," says Epstein.

Bartlit says he keeps the partners at his firm happy not just by paying them well, but also by giving them the chance to do what they most love to do — fight in court. "People get in court all the time," he says. "I think something like 94 percent of our lawyers took a witness to the trial last year." He believes the same holds for players like James; the money has to be there, but the real gratification is in offering them a chance to compete and win.

Dan Gilbert has tried seduction. Three years ago, the Cavaliers opened a $25 million, 50,000-square-foot, state-of-the-art practice facility, which just happened to be convenient to James's 33,000 sq.-ft. home in Summit County. Since the season ended, both the team's general manager and coach have left, fueling speculation, denied by Gilbert, that the moves were made at James's behest.

The Cavaliers and their fans have been shameless — and shrewd — in selling James on the sentimental appeal of staying home. A billboard near the Cavaliers' Quicken Loans Arena hopefully declares, "Born Here. Raised Here. Plays Here. Stays Here." Both President Barack Obama and NBA Commissioner David J. Stern have noted the appeal of James re-signing with Cleveland.

Yet when money is equal and emotional appeals have been exhausted, it comes down to winning, a currency of its own, and one that James has said he is most passionate about. Outside of professional sports, few things are as unambiguously precious as a championship. Here, Cleveland is at a distinct disadvantage; of all the teams in the NBA, only the Cavaliers have proven they can't win it all with James — seven years, no titles. Chicago has the most talented supporting cast and can offer James his best chance at an immediate trophy. New York owns the greatest story line — a marquee franchise starved for a hero — and the city itself promises to make winners of anyone who moves there. On paper, Gilbert and the Cavaliers can't win, yet they clearly can't afford to lose. The reason they're so vulnerable is the same reason they have a shot — because it all comes down to one guy. The only thing worse than a LeBron problem is no LeBron.

Draft day

NBA commissioner David Stern congratulates LeBron James after he was chosen by the Cleveland Cavaliers as the No. 1 overall pick of the 2003 NBA Draft.
(Ed Betz / ASSOCIATED PRESS)
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ESPY

A month after being selected No. 1 overall by the Cavs, LeBron James presents an award with basketball great Julius Erving at the 11th annual ESPY Awards show.
(Kevork Djansezian / ASSOCIATED PRESS)
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First sneakers

The first official sneaker for LeBron James. In high school, LeBron wore the signature shoe of icon Michael Jordan. Now he is being compared to his idol right down to his sneakers.
(Rick Bowmer / ASSOCIATED PRESS)
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First game

In his first NBA game against the Sacramento Kings, LeBron recorded 25 points, nine assists, six rebounds and six steals and shot 60 percent from the field.
(Richpedroncelli / ASSOCIATED PRESS)
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41 points

On March 27, 2004 against the New Jersey Nets, LeBron became the youngest player to score 40 points in a game (19 years, 88 days, as he recorded 41 points.)
(Tony Dejak / ASSOCIATED PRESS)
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King vs. Melo

R.O.Y.

Cavs guard LeBron James answers questions during a news conference announcing him as the youngest player to be named NBA Rookie of the Year (19 years of age).
(Ron Schwane / AP)
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Triple-double

On Jan. 19, 2005 against the Portland Trail Blazers, LeBron became the youngest player to record a triple-double (20 years, 20 days). He had 27 points, 11 rebounds and 10 assists.
(Rick Bowmer / ASSOCIATED PRESS)
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56 points

On March 20, 2005 against the Toronto Raptors, LeBron became the youngest player to score 50 points in a game (20 years, 80 days) with 56.
(Frank Gunn / ASSOCIATED PRESS)
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Average of 30 points

All-Star MVP

LeBron James of the Eastern Conference holds up the MVP trophy at the end of the 2006 All-Star game at the Toyota Center in Houston. He became the youngest player to win the award (21 years, 55 days).
(James Nielsen / AFP/Getty Images)
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Hot streak

2007 NBA finals

Although LeBron led his team to the NBA finals, he could not get them past the San Antonio Spurs. The Spurs won the best-of-seven series 4-0.
(Jeff Haynes / AFP/Getty Images)
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ESPY host

LeBron co-hosted the ESPY Awards at the Kodak Theatre in Los Angeles on July 10, 2007, and also hosted the season premiere of Saturday Night Live in September.
(Nick Ut / ASSOCIATED PRESS)
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On the bandwagon

LeBron James holds up his New York Yankees hat during the fourth inning of Game 1 of the American League Division Series baseball game between the Yankees and Cleveland Indians. LeBron received a lot of criticism from Cleveland fans for being a Yankees fan. LeBron later explained that he grew up being a fan of the Yankees, Dallas Cowboys and Chicago Bulls.
(Amy Sancetta / ASSOCIATED PRESS)
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Second All-Star MVP

10,000 points

On Feb. 27, 2008 against the Boston Celtics, LeBron became the youngest person to score 10,000 points in his career (23 years, 59 days).
(Elise Amendola / ASSOCIATED PRESS)
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Knicks game

On March 5, 2008, LeBron tallied 50 points, eight rebounds and 10 assists against the Knicks, becoming the third player since the NBA-ABA merger to record a 50-point, 10-assist game.
(Al Bello / Getty Images)
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All-time scorer

On March 21, 2008, James scored 29 points against the Raptors, passing Brad Daugherty as the all-time leading scorer in Cavaliers history.
(Mark Duncan / ASSOCIATED PRESS)
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Summer Olympics

James, along with the rest of Team USA, reclaimed the gold medal at the 2008 Beijing Olympics, defeating Spain 118-107. He had 14 points, six rebounds and three assists in the gold-medal game.
(Dusan Vranic / ASSOCIATED PRESS)
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King of New York

Two days after Kobe Bryant scored 61 at Madison Square Garden, LeBron puts up 52 and a triple-double as the Cavs beat the Knicks, 107-102, on Feb. 4, 2009.
(Nathaniel S. Butler / NBAE/Getty Images)
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First league MVP

LeBron James holds up the 2008-2009 MVP trophy before the Cavaliers play the Hawks in the Eastern Conference semifinals. He averaged 28.4 points, 7.6 rebounds and 7.2 assists in the regular season.
(Gregory Shamus / Getty Images)
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Second league MVP

LeBron James became a two-time MVP winner in his final season with the Cavaliers, averaging 29.7 points, 7.3 rebounds and 8.6 assists during the 2009-10 regular season.
(Bill Kostroun / AP file)
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The 'Decision'

LeBron James, the NBA's reigning two-time MVP, ended months of free agency speculation and suspense by telling the world live on ESPN on July 8, 2010, that after seven seasons he's leaving the Cleveland Cavaliers to join Dwyane Wade and Chris Bosh in Miami.
(Rich Arden / AP)
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LeBron turns up Heat

LeBron greets fans as he is introduced during a Miami Heat welcome party at American Airlines Arena on July 9, 2010.
(Doug Benc / Getty Images)
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2011 NBA finals

LeBron James and the Miami Heat held a 2-1 series lead against Dirk Nowitzki and the Dallas Mavericks, but lost the NBA Finals in six games.
(Hans Deryk / Reuters)
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2012 NBA finals

LeBron James led the Heat in scoring in each game as Miami beat the Oklahoma City Thunder in five games to claim James' first NBA championship.
(Nathaniel S. Butler / NBAE/Getty Images)
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2012 NBA finals MVP

James was voted the unanimous NBA Finals MVP after averaging over 28 points, 10 rebounds, and seven assists per game during the series.
(Joe Murphy / NBAE/Getty Images)
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2012 Summer Olympics

When the USA won gold in London, James joined Michael Jordan and Scottie Pippen as the only players to have won an NBA championship and an Olympic gold medal in the same year.
(Pascal Le Segretain / Getty Images)
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Editor's note:
This image contains graphic content that some viewers may find disturbing.